When an electromagnetic wave propagates along the length of a wire, the electromagnetic wave, generated by the movement of electrons within the wire, penetrates into the wire somewhat, this penetration being a result of the "skin effect" phenomenon. The intensity of the signal that penetrates into the wire decreases exponentially with distance into the wire. The penetration into the wire, called the "skin depth", is given by: ##EQU1## .delta. (delta) is the skin depth (meters); .apprch. (sigma) is the electrical conductivity (mhos/meter);
.mu. (mu) is the relative magnetic permeability (1.0 for air); and PA1 f is the frequency in hertz.
For copper, equation 1 yields approximately: ##EQU2## The above formulas can be found in most electromagnetic theory text books.
There are two important phenomena associated with skin depth:
1. The signal strength decreases exponentially with distance into the wire, as follows: EQU S=S.sub.o e.sup.-L/.delta., (3)
where
S is the signal strength inside the wire, at a depth L below the surface;
S.sub.o is the signal strength at the surface of the wire;
.delta. is the skin depth given by equation 1 or 2 above;
L is the distance into the wire where the signal S is measured; and
e is the base of natural logarithms.
2. The speed of propagation of electromagnetic signals in good conductors is drastically reduced from the speed in a vacuum (3.times.10.sup.8 m/sec). The speed of propagation in a conductor (v) is exactly that required for the skin depth to be equal to the wavelength (.lambda.) divided by two pi, or expressed mathematically, ##EQU3## EQU v=f.lambda.. (5)
Thus, by combining equations 4 and 5, EQU v=3,167 (f/.sigma..mu.).sup.1/2 meters/second. (6)
For copper, this results in a speed of propagation equal to ##EQU4## In copper, the speed of propagation of an electromagnetic wave is approximately: 1.9 meters per second (m/sec) at 20 Hz; 13 m/sec at 1 kHz; and 60 m/sec at 20 kHz.
Thus, a signal propagating into the interior of a conducting wire experiences a substantial delay (one radian of phase for each .delta. into the wire) and also experiences an attenuation by a factor of e for each .delta. into the wire.
It is possible that such a signal, upon reaching the other side of the wire, can reemerge from the wire and continue propagating down the wire. But due to the very slow speed of propagation within the wire, this wave that has traveled through the wire and emerged from the other side may be substantially and audibly delayed.
The purpose of this invention is to minimize audible effects caused by such propagation through the thickness of a wire and reemergence from the other side.
The equations above show that the skin depth (.delta.) depends on the frequency of the audio signal, as well as the conductivity and magnetic permeability of the conductor. The vast majority of electrically conducting wire is made of copper, for which the above formulas yield a skin depth of approximately: 15 millimeters (mm) at 20 Hertz, 2 mm at 1 kHz, and 0.5 mm at 20 kHz. The range of human hearing is usually quoted as 20 Hz to 20 kHz, although many audio equipment designers strive for a greater bandwidth in order to ensure high quality in the audible range, in addition to addressing those individuals whose hearing may be better than normal.
Copper wires used in the circuitry of audio recording and playback processing and/or amplification equipment, including preamplifiers, mixers, amplifiers, compact disk players, musical instrument electronics, phonographs, tuners, tape and cassette players, microphones, equalizers, loudspeakers, headphones, etc., and the interconnects among these components, are generally considerably thinner than the skin depth of copper at all but the very highest audio frequencies. Thus, as mentioned above, an electromagnetic wave, representing an audio signal, carried by a typical copper wire in an audio circuit can easily propagate through the entire width of the wire, emerge from the other side, and then interfere with the electromagnetic wave present on this other side, perhaps producing audible distortion of the resulting audio signal. This distortion is due to the time delay encountered by the signal while propagating through the thickness of the wire. This distortion is not the "harmonic distortion" that is frequently measured and used as a figure of merit for audio equipment; rather, it is a form of phase distortion, since the phases of different frequencies will be affected differently. Therefore, this distortion mostly affects the transients in music reproduction, which contain a wide range of higher frequency signals. It does not appear to be previously realized that non-zero skin depth can cause this type of distortion.
Since the velocity of propagation through the wire varies with frequency in accordance with equation 6, the resulting signal suffers from the phenomenon of dispersion, wherein different frequencies in a signal propagate at different speeds through the thickness of a conductor and consequentially a sharp precise pulse becomes fuzzy and smeared out over time.
Consider for example a copper wire of 0.5 mm diameter (a medium to large diameter wire when used to connect components, such as resistors and capacitors, in an audio circuit). The calculated skin depth at audio frequencies is much larger than the wire diameter. At the lower audio frequencies, there is little distortion because the phase delays are negligible with respect to the periods of the lower frequencies. However, at the high audio frequencies, the interference caused by the addition of out-of-phase electromagnetic waves may become audible since the propagation delays are more significant with respect to the periods of the higher audio frequencies. Specifically, the time delays due to the electromagnetic wave passing through a 0.5 mm diameter copper wire are approximately: 270 .mu.s at 20 Hz (20 Hz having a 0.05 second period); 38 .mu.s at 1 kHz (1 kHz having a 1,000 .mu.s period); and 8.5 .mu.s at 20 kHz (20 kHz having a 50 .mu.s period).
To virtually eliminate the deleterious effects of the audio signal propagating from one side of a wire to the other, the wire should be made as thick as several skin depths at the lowest frequency, typically about 20 Hz. The reason for desiring to make the wire very thick with respect to the skin depth is that, according to equation 3, the interfering signal that propagates through the wire is then significantly attenuated--by a factor of 10 for every 2.3 .delta. of thickness.
Although thickening the wire (with respect to skin depth) will also increase the phase delay, the goal is to employ the increased attenuation to eliminate the resulting distortion. For copper wire, the required thickness would be several centimeters, which is impractical in audio circuits.